Finite Group DatabasebetaFinite Group DatabasebetaOrder 27392.
170 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C107 | D16 |
| commutator | C16 | C42×C107 |
| Frattini, cosocle | C22×C16 | C22×C107 |
| socle | C22×C107 | #357 |
| prime radical | C23×C107 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C107 ◁ C22×C4×C107 ◁ C22×C8×C107 ◁ C22×C16×C107 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×C32×C107 | C4 | semidirect |
| 11. #368×C107 | C4 | semidirect |
| 67. #7473 | C107 | direct (N × H) |
| 75. C107 | #7473 | direct (N × H) |
| 81. C2×C32 | C4×C107 | semidirect |
| 83. #368 | C4×C107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C107 | 2 |
| C2×#368×C107 | 2 |
| C107×#2158 | 2 |
| #7473 | 107 |